Comment #34 on issue 1823 by ronan.l...@gmail.com: integral.atoms(Symbol) should introspect
http://code.google.com/p/sympy/issues/detail?id=1823
The useful sets of symbols are 1) the free variables (i.free_symbols in #c29) and 2) the integration variables bound by the object (i.variables in #c29). 1) is needed for derivatives and the like, while 2) can be useful to perform substitutions on the integrand. I think that 'free_symbols' and 'variables' are appropriate names, respectively, while 'symbols' suggests 2) rather than 1) so I don't like the idea of using it for 1).
+1 on using dummies, though I don't think it would solve the problems you mention: we'll still have integrand.has(dummy) which implies integral.has(dummy).
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